Q. 134.8( 4 Votes )

# For what value of k does the system of equations

x + 2y = 5, 3x + ky + 15 = 0

have (i) a unique solution, (ii) no solution?

Answer :

(i) Given: x + 2y = 5 – eq 1

3x + ky + 15 = 0 – eq 2

Here,

a_{1} = 1, b_{1} = 2, c_{1} = - 5

a_{2} = 3, b_{2} = k, c_{2} = 15

Given systems of equations has a unique solution

∴ ≠

≠

k ≠6

∴ k ≠ 6

(ii) Given: x + 2y = 5 – eq 1

3x + ky + 15 = 0 – eq 2

Here,

a_{1} = 1, b_{1} = 2, c_{1} = - 5

a_{2} = 3, b_{2} = k, c_{2} = 15

Given that systems of equations has no solution

∴ = ≠

Here,

=

Here,

k = 6

∴ k = 6

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